The eventual heat death of the universe is an awful time to be alive considering you wouldn't have long left after the last star finally fades away.
In this scenario there is a small group of about a dozen human survivors who live in a colony on an earth-like planet that orbits the last star to burn out. The group know of their impending doom and have time to prepare for it, about 10 years (but feel free to adjust this time if you think of something cool).

Now I fully expect answers that lead to the eventual death of everything from this scenario but what would this group need to do in an attempt to continue existing for as long as possible in a universe with no heat?

Note: This would be trillions of years into the future so feel free to go a little crazy with future science, as long as it makes sense. It would also be interesting to see how a race of humans with current-day technology could survive in the same conditions.

$\begingroup$The "Heat Death of the Universe" is not "a universe with no heat", but rather, a universe where everything locally has the same amount of heat. Being cold won't be your problem, having no exploitable energy differential (ie., no Power) will. You won't even have enough power to run your own body...$\endgroup$
– RBarryYoungFeb 4 '16 at 20:57

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$\begingroup$And the real problem, is that according to our current understanding, the "Big Rip" (expansion due to Dark energy) will get us long before the Heat Death does, and it's appears to be a lot harder to forestall.$\endgroup$
– RBarryYoungFeb 4 '16 at 21:00

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$\begingroup$How can entropy be reversed? multivax.com/last_question.html (Seriously, I'm the first person to link to this? I must be missing some replies...)$\endgroup$
– LizardFeb 5 '16 at 15:33

$\begingroup$@Renan Another problem with this Q, which is even a bigger problem for trying to get better answers with a bounty, is that people are not even sure that there will be a heat death, and even among all those who believe there will be one they cannot be sure what exactly it would be like. You are essentially asking for better answers for a question about something unknown. On top of that, since we accept fiction here, there is already a good answer, which also includes the fact "You can't, since by definition there is no heat death if you are still existing in a capacity to talk about it."$\endgroup$
– LoduwijkNov 19 '18 at 19:15

26 Answers
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I mean, literally. As in "get out of the universe". The heat death of our universe is by definition not a survivable event. That's the bad news. The good news is that it takes a very, very long time to happen. So a technological society has time to develop technological solutions to the problem.

Some things that might work are:

Cross over to an alternative universe. Multiverse theory is endorsed by a surprisingly large number of prominent physicists. So let's assume the physicists are right, that multiple universes exist, that at least some of them still have a few trillion years left in them when our universe is grinding to a halt, and that science has advanced to the point where it's possible to travel between universes at will. Why struggle to survive in a dying universe when you can just move next door and start over on a new planet?

Return to a previous time in the current universe. So multiverse theory didn't pan out despite its prominent endorsements; who cares? Perhaps wormholes are real and capable of traversing both space and time. If they are, it's plausible that a technological society will learn to control them before the universe's heat death occurs. And if they do that, they can use them to travel to any desired place and time within the current universe. So they can just pick a more hospitable moment in time, and go there. But might lead to interesting cyclical dilemmas as repeated generations keep jumping back in time to avoid facing the heat death of the universe (only to find some subsequent generation already camped out in their chosen real-estate).

Jump in a black hole. So both multiverses and wormholes turned out to be fake; guess we're screwed. But no need to wait around to die an icy death. Instead find the nearest black hole (or use your stockpile of doomsday devices to create one) and jump in. At least you get to go out on your own terms. And who knows, maybe black holes are actually survivable or will transport you to somewhere a little less doomed. If nothing else, it won't be boring and perhaps relativistic time dilation will give you a good view of the universe's final moments.

Invite some guests

Kind of an inversion of the previous approach, but maybe multiverses do exist but we're not able to safely transport living things from our universe to another. That doesn't necessarily mean we can't snag a fresh sun or two every now and again. You know, just enough to keep a tiny ember burning in our universe.

Heat death doesn't occur until you reach maximum entropy, which is something that you can hold off indefinitely if you're able to pull in even relatively small (say, on the order of an M-class star) clumps of matter every few billion years. If you've got the technology, and a power source for it (the big question is whether it can be possible to pull a star from one universe to another using less energy than the star will generate over its useful lifetime), you can wait it out.

Come to think of it, you can wait it out regardless since the heat death of the universe can't occur until well after any warm-blooded life forms have ceased functioning. The most you can ever observe is the prelude.

$\begingroup$The time dilation created by jumping in a black hole is infinite. So you would actually perceive the entire rest of the universe in a single instant, much like light always does.$\endgroup$
– JekowlFeb 2 '16 at 16:36

$\begingroup$There won't be any black holes around if this is the "last star" before heat death. They will have all evaporated. The presence of black holes would be a strong indicator that heat death is still a seriously looooooong way off.$\endgroup$
– spenderFeb 3 '16 at 11:59

$\begingroup$This is the only correct answer from a scientific perspective.$\endgroup$
– dotancohenFeb 2 '16 at 14:23

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$\begingroup$@dotancohen - I don't know about that, but its definitely the funniest. I ROFLed at the concept of stars producing entropy like mad. If Douglass Adams ever needed a new villain to replace his Krikitteers, a race that goes around "putting out" stars to stave off the Heat Death of the Universe would be perfect.$\endgroup$
– T.E.D.Feb 2 '16 at 14:47

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$\begingroup$Man this has to be Daoist philosophy!$\endgroup$
– busukxuanFeb 2 '16 at 19:13

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$\begingroup$Throw black holes at them. Black holes radiate much slower than a star. That would put them out. (Indeed, producing micro-black holes is plausible. They would eat up a sun quickly.)$\endgroup$
– PyRulezFeb 2 '16 at 20:42

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$\begingroup$@Sobrique - I'll answer that question once I figure out how to divide by zero.$\endgroup$
– T.E.D.Feb 4 '16 at 15:59

I think the question is fundamentally ill-posed. As long as there are humans alive somewhere, the universe is millions to the power of millions of years away from the "heat death" (which is not at all an agreed-upon or well-understood thing).

The heat death (if we assume it is well-defined) is definitely not "when the last star fades away". It's waaaay later than that, at least after the final supermassive black hole has evaporated due to Hawking radiation, which would take on the order of 10$^{100}$ years after the last star dies.

$\begingroup$And even then, if you're still around to observe it, it hasn't happened yet. The human body (and any nuclear reactors they have with them) are wonderful black body radiators. They make shitty stars, but they're still warm. ;) Also...[rough math] $10^{100}$ is how many proton half lives? 3? There'd still be a good quantity of mass bubbling about (1/8th the amount than when the the stars died, easily 1/64th of present day, which is still a lot [citation needed]).$\endgroup$
– Draco18s no longer trusts SEFeb 2 '16 at 15:34

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$\begingroup$+1 to this. The end of the stelliferous era is merely billions of years from now whereas the Heat Death of the Universe is quintillions of years away$\endgroup$
– RichardFeb 2 '16 at 23:17

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$\begingroup$If you're going to go "hard physics", I'd like to see some back of the envelope estimates for your claim about the relative time it will take for stars to die vs. black holes to evaporate. Could you provide something like that?$\endgroup$
– DanuFeb 3 '16 at 19:04

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$\begingroup$@Danu if you look at the link posted by Richard above, you get a pretty good idea. In about 10$^{15}$ years, no solar systems will exist in the universe anymore. That's a ridiculously tiny number next to 10$^{100}$.$\endgroup$
– semi-extrinsicFeb 3 '16 at 21:20

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$\begingroup$You're assuming the humans haven't changed into something entirely different trillions of years in the future.$\endgroup$
– DCShannonFeb 4 '16 at 20:30

$\begingroup$Of course that computer is plugged in to a power source, and its power usage is increasing the entropy of its surrounding universe, so this solution really only postpones the problem... :)$\endgroup$
– Jeremy FriesnerFeb 4 '16 at 23:55

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$\begingroup$How do we even know their universe works that way?$\endgroup$
– Eric JohnsonFeb 5 '16 at 0:04

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$\begingroup$Please don't do that until you know what you are doing. The risk of accidentally crashing the simulation is not to be taken lightly.$\endgroup$
– kasperdFeb 6 '16 at 23:15

I think the question implies a paradox that can't occur. The heat death of the universe is not when the last star goes out, it's when the universe reaches maximum entropy.

By definition then, there's no way of 'surviving' the event, because you'd have to be dead in the first place for the condition to have been reached. Dead, decomposed and the energy you released into the ground dissipated universally. You get the idea.

But lets assume the question is: can a civilization survive the extinguishing of the last star. Well, yes. Aside from any local reserves of fissile material, the planets themselves are still orbiting, so there's still masses (sic) of energy sitting in gravitational wells, waiting to be harvested. And that dead star is still rotating the galactic center, and that's still caught up in some amazingly long range interactions with other galaxies. And so on. Extracting usable work from all this energy will be a significant challenge however, but if the motivation is there...

$\begingroup$With all due respect to the answer, I don't think this was the question. You are correct that the existence of live, let a lone a star, implies that true heat death is far away; but for the sake of the argument we must assume that this star has been scraped together artificially from the last fusable material inside the event horizon with great effort, and that was that. All the energy stored in spin and orbits etc. is cosmologically negligible. There is enough energy differential available though to build one last device, or space ship, or whatever.$\endgroup$
– Peter - Reinstate MonicaFeb 6 '16 at 10:57

The ratio between number of years in your scenario and the actual heat death is a 1 followed by about 986 zeros. You're a bit early.

The classical physics definition of "the heat death of the universe" is the moment when the universe reaches "thermodynamic equilibrium (AKA maximum entropy)." which means that there are "no net macroscopic flows of matter or of energy."

Let's presume that the universe refers to the entire universe and not just your personal "observable universe" for simplicity's sake.

Note that there are numerous theories and wild ideas in physics that suggest that either this point would literally never be reached due to other events or that it would decrease again afterwards and thus multiple heat deaths might be possible.

Note above the word "macroscopic". There is, in practice, a lot happening below that scale and if you accept the concept that life can be realised as dynamic information, then it is possible to assume that after many, many trillions of years of technological advances we might figure out a way to live down there at that scale.

We might not even notice the heat death occurring? (Oh, was that this week, I though I set a reminder...)

If your civilisation has access to sub-macroscopic technology, then by definition you can use any sub-macroscopic based escape path without blocking the heat-death.

That could mean living down there at that scale or transporting yourself to a different universe.

While another poster suggested "jumping back" to previously stable points in time, it is worth mentioning that we don't really know what time is. Therefore, there are properties and functions of time with applications that we aren't even aware of yet.

For example, once you can control time, you can probably exert some control over space-time. Infinite control means you could craft physical laws that recirculate energy throughout the universe in a predictable format, like a river with walls. This could be a corollary to Einstein's "Cosmological Constant," where the universe expands as it does now, contracts a bit to harvest and recirculate the energy, expand again, and so on.

Two issues, however:

1: The energy required to exert sufficient control over space-time may exceed the available cosmic energy required for infinite existence.

2: Space-time control could have "leaks" of its own, resulting in the same eventual heat death. You could still get a few trillion-trillion years or so of existence, which ought to help a sufficiently advanced civilization come up with a more permanent solution.

As a final note: we are considering options based on what we know today. Thomas Malthus predicted the end of civilization as population exceeds resources, however he lived in a time when the primary economy was making food and the primary fuel was food and muscle (livestock, slaves, etc). It is unlikely he could have foreseen a future where robots harvest crops from year-round solar-powered greenhouses. It is therefore reasonable to expect that our limited understanding of the universe denies us the vision to see solutions beyond the tools we are aware of.

Given how long humans have existed and how little the time, in geologic terms, it took for us to go from hunter-gatherers to the Information Age, I suspect that if we can avoid nuclear, environmental, or biological apocalypse, we will figure it out in time.

$\begingroup$Great answer. Such a shame your username wiped my hard-drive, so now I don't have a mouse driver with which to click the upvote button. I suppose I'll have to restructure the laws of physics again! (So annoying)$\endgroup$
– wizzwizz4Feb 2 '16 at 18:03

There's an odd mathematical construct you can strive for, to survive as long as you need. The key is that heat death is not an event, but a slow predictable decline in energy.

If you can accurately measure how much usable energy you have (lif you have to err, err on the lower side), and you can spend energy proportionally to that amount, you end up with an exponential curve of dwindling energy, which mathematically never ends.

The tricky part is when you are dependent on processes which are not proportional like that. For example, we are currently very dependent on activities which rely on quantized behaviors, such as the emission of photons. Those events will have to be more and more rare as the energy levels decrease. You would also likely choose to concentrate your energy in a smaller and smaller portion of your space, in order to permit at least a small portion to be using such quantized energy. In fact, this has lead to two competing extremes as to how to accomplish this goal. There is the continuous process, where you try to keep a fluidly decreasing amount of energy usage, and the discrete approach, where you subtly collect energy for as long as needed to permit one quick burst of a finite length of energy. Presumably whatever the final solution will be will involve a cross between both of these approaches.

The hard part is knowledge of the heat death: you don't have it. There is no way for science to know that heat death will occur, as opposed to us discovering that our mathematical models which proved heat death will occur were wrong. Sure in our 359 years or so of modern science and thermodynamics, we're pretty sure that's the direction things go. We have another 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 years before galaxy sized black holes vanish, and I'm not even going to write out all the zeroes in the $10^{10^{56}}$ years before quantum tunneling might start poking holes that let us into other universes, by our theories. We have a long time to find out that we have an incomplete theory. The hard part will be not developing a survival scheme that assumes we've seen it all, and starts down the path of exponential decay to live forever like Nietzche's Last Man. We would need to continue to reach out and observe the dying universe, looking for hope. If we find it, we need to be about to harness it to build the best world we possibly can.

You can imagine how horrible it would be to find that there was a god like physical entity just outside our perception, nurturing us along, only for us to give up on ever joining them. More interestingly, the smaller the civilization gets (as heat death looms), the smaller such an entity could be and still be perceived as having godlike powers! When the universe is facing proton decay, and a civilization is trying to simply hold onto the tiny quantum blurs that keep it alive, imagine how powerful you or I would seem, happily collapsing trillions of waveforms every moment just to pick up a glass of water, nevermind the trillians of irreversable chemical reactions going on in our synapses to feel like we are thirsty.

Thus, the balance. The more energy spent exploring the world outside, the harder it is to maintain an eventual exponential decay to live forever, but if you squirrel yourself away in exponential decay, that's all she wrote. You have to strike the balance between the two.

Fascinating how life itself has a tendency to be able to balance the nuances of continue procreation for an astonishing number of generations, while never ignoring the world around it, constantly evolving based on new observations and discoveries (even if those discoveries are simply radiation breaking DNA strands). Perhaps it is life itself that will one day strike this balance. Imagine what life could do if it reached out into the quantum world, instead of being shackled to classical physics. Maybe the Gaia theorists are on to something.

$\begingroup$"in our 359 years or so of modern science and thermodynamics, we're pretty sure that's the direction things go" Not that sure. We do already have several other theories that are at least as well supported as heat-death (and none of them are as well-supported as you seem to think heat-death is; this is just not an easy thing to observe and measure when it only happens once, and not yet). John McNamara's post has a link that lists a few examples.$\endgroup$
– Matthew NajmonFeb 12 at 18:15

Not previously addressed issue:

Due to the acceleration of the inflation of cosmological space there exists a point in time where the expansion of space exceeds the speed of light. In such a universe there may still be particles flying around and light zipping off in Directions and stuff still "happening" but space is inflating so rapidly that even photons cannot interact with each other, much less anything else (causality is limited by the speed of light). In such a universe, matter as we know it cannot exist. Your heat death colonists will find their bodies being ripped apart by the sheer inflationary aspect of space itself (assuming somehow remaining intact until this point).

Notably this effect will likely cause problems long before the rate reaches the speed of light, but I am unsure how much sooner, or when it occurs relative to classical Heat Death. I can only say for certainty that such a time exists where nothing can interact with anything, and that is currently not the case, ergo a point in time exists between these two extremes where atoms, molecules, and larger structures themselves will be torn to shreds by the expansion of spacetime as it overcomes the bonds holding things together.

$\begingroup$I've seen descriptions of the expanding Universe as varying from "it will rip subatomic particles apart" to "only non-gravitationally bound objects will separate" (which means our Local Group of galaxies will continue to hang out in our light cone, but the rest of the Universe accelerates away from us faster than the speed of light).$\endgroup$
– Jim2BFeb 4 '16 at 5:30

$\begingroup$I think both of those will happen, @Jim2B , but at different times. The gravitationally bound lightcone scenario would happen first (local group distances are still close enough that the acceleration between them is < c) and only later will the latter happen (once the acceleration between subatomic particles > c). I just don't know the timescales involved.$\endgroup$
– Draco18s no longer trusts SEFeb 4 '16 at 15:13

The answer not yet mentioned: don't do anything, just wait until the random fluctuations bring the Universe arbitrarily close to your current state according to the Poincaré recurrence theorem. In fact, you will return infinitely many times, that means you cannot be sure you are not already beyond the previous heat death. It is indeed very probable.

$\begingroup$If the universe can in fact return to any previous state due to random chance, the odds that you already survived a 'heat death' would be almost certain: (infinity - 1) / infinity$\endgroup$
– AllenFeb 2 '16 at 21:25

Create (simulate) a new universe

Similar to the "Hack the Universe" answer, but instead of exploiting a bug within the current universe, just create a new universe within the current universe. Scientist will have a lot of time before the heat death of the universe to create faster and faster supercomputers and will be able to create a computer so fast and powerful that it will be able to simulate an entire universe (and do it more efficiently than the real universe). The computer could simulate events of a universe at a much higher speed than the current universe. In this way, one year in the real universe could be the same as thousands of years in the simulated universe. And during this time the scientists can find ways to improve the speed of the simulation, making it lasts millions or billions of years longer.

3) the question itself really means nothing. It has massive implied circumstances that are hidden in the choice of words:

what does "survive" mean?

for how long?

in what form?

what else exists that you survive into?

back to the physics first: "heat death" is, as someone notes, achieving maximum entropy. That means that every piece of matter in the universe (and it's all still here, if it hasn't been converted into iron and energy by fusion), has reached background radiation temp (currently 3 deg Kelvin, not 0). Energy cannot dissipate any further, because it has gone as far as it can go. It can't be destroyed (remember that from grade school science), so it has achieved flat uniform distribution over the entire universe.

For that to be true, "you" have dropped to 3K as well. So you aren't alive, in any sense of "alive" that we currently think has meaning.

But of course "you" ("we") have already long since moved beyond having a corporeal existence, so "atoms" aren't interesting any more.

we have no current understanding of "dark matter", or "the inside of black holes" or "the inside of quasars", who knows what other exotic phenomena exist?

and this question suffers from incomprehension consider that we can't even imagine what the other side of the sci/tech singularity is going to look like: in another thousand years, if not sooner, we aren't going to be "human" any longer, in the current sense of humanity. What is that going to mean? (this, I think, is a central failing in science fiction, which I read a lot of: in a story set hundreds or thousands of years from now, people haven't changed a bit. Seriously? I get that it would be impossible to write a comprehensible story about those characters in terms we could understand today, but really, way too much SF has characters essentially from "today" transplanted into a new/different setting that will actually be WAY more exotic than a person from Pittsburgh going to Mexico City.

one additional thing: in a continually expanding universe, with a fixed amount of mass/energy, the background temp will drop over time, so that what we measure as 3K now will go down, but it can't ever reach zero, because that would mean the universe stretched to mathematical infinity, which isn't possible.

and other basic physical forces would still exist. If the universe reached 3K, does it then begin to collapse? Gravity isn't going to go away.

relevant stories: Tau Zero, as mentioned...In Iron Years, Gordon Dickson. Neither address the original question, but are interesting sidebars

$\begingroup$Welcome to Worldbuilding! I have some constructive criticism for you. You have some very good points mixed in with your, otherwise, conversational answer. Hopefully you can edit it so the salient points float to the top over the fill. This isn't a forum, if you're going to ask questions you want an answer to, do so in the comments of the original question.$\endgroup$
– SamuelFeb 2 '16 at 18:32

First solution: stand still and await your fate, there is nothing you can do when the only thing in the universe is one $0K$ iron atom$/500km^2$.
Second solution and since they manage to keep an hearth-like planet until this time, well they might get energy out of nuclear reactions of it's constituent. Everything that is not iron can release energy that way. Then when you are out of dirt start to use other people, when you are out of people well use your limbs, when you are out of limbs you are officially doomed.

Note that heat death is an absolute end, all you can do is delay the inevitable.

Other solution: dualism. If the soul is immortal and does not need energy you bypass the question. You can make a story about ascending to that state to "survive" the end of the universe.

"you gotta use a magic stick": find a way to change the laws of physic through whatever technology. Entropy in a closed system CANNOT decrease, wave your hands and remove entropy.

"It's not heat death yet": transform iron into anti-iron, spoof magic: direct mass to energy conversion. you just got a couple quadrillion years before there is effectively no matter left in the whole universe.

Last solution: reverse the flow of time? that's the only way you can decrease the entropy of the universe without rewriting physic and since time travel is common in sci-fi I guess that could be a good solution. You can as for example create a time loop where the end of a day is the beginning of the same day.

$\begingroup$and by iron I mean iron. It can't fission nor fusion without energy from an external source. In an universe where all nuclear energy is depleted (because of those huge nuclear factories people call stars) that's the only thing left.$\endgroup$
– NyashesFeb 3 '16 at 9:33

Embrace the Cold!

So the universe is going cold, right? Abandon all of your current concepts of life and humanity and become one of the Cold Ones, creatures able to survive, nay, thrive in this new cold universe without heat or entropy! Make them hardy enough to thrive in the cold between dead stars and maybe even sturdy enough to survive a big crunch/big rip scenario, possibly surviving into the next universe.

If they do make it that far, do they embrace their anti-heat/anti-entropic nature or go back to being warm humans?

avoid it

With all energy sources run out, you can still keep a prepared system that's in equilibrium.

There is a concept called reversible computing. Random changes can make the calculation run forward or run backwards. To ensure progress you need some tiny sink of entropy, and maybe this can still be found using some quantum vacuum phenomena, or some symmetry-breaking operation.

But even if no such loophole exists, you literally have forever: the calculation will progress forward and backward at a random walk, at some point proceeding forward arbitrarily far.

To the software entity, he still thinks and experiences time. But his time runs forward and backward in a random manner: thinking thoughts and laying down memory, then un-thinking and restoring memory to the earlier state! But eventually it gets forward, and reoccuring the exact indistinguishable state is no different from having it exist only once.

Conserve energy
Our future ancestors have invented a way of preserving energy in super batteries that don't discharge over time! They created a network of colonies in which we incase all stars with dyson spheres that let the colonies utilize their star systems energy meanwhile sending their spare energy to the central government as a tax.

Once heat death is impending and colonies cant move to another solar system since all stars are "going out" we will all migrate to the central government,create a planet of our own which its core is literally a huge battery.

A floating space sanctuary containing the energy of a couple billion stars. We will just breed and mess about on our planet-writing poetry and living life.

Nothing will actually happen because the past is just as real as the present and the future. So, the universe in the heath death state just exists out there just like the early universe and the universe in the state we experience today.

When faced with the prospect of dying, what will actually happen is that you'll survive with memory loss about that fate, you'll most likely end up somewhere back in the past where the things that you now consider as already having happened, haven't actually happened from that other perspective. These are just possible things that could happen in the future. Also, the outcome of these events doesn't have to be the same, as we're living in a quantum multiverse.

And so just as there wasn't any such thing as 'before' the big bang, there is no such thing as 'after' the heat death of the Universe - time will have 'run out'. Think of it like a clock winding down - it runs steadily slower and slower, until it stops entirely... but the clock hasn't vanished, it's still right where it always was.

So really - there's nothing to survive, because it doesn't actually end - we won't perceive the ticking slowing either, because our temporal perception is 'locked in' at 1 second per second.

One day, everything will just stop entirely, about the point where the Universe turns into a rather cold and thin soup. This is an extremely long way off though, as almost by definition - the very existence of a person means there's quite a lot of 'unspent' entropy left.

Aquire a Cosmic String(no relation to the strings in string theory.) Cosmic Strings are an extremely rare topological defect that are narrower than a proton, but light years long. They are incredibly dense, causing extreme space time distortion near them. By finding one, spending several billion years traveling to the nearest one, and then somehow grab both ends of the string, cross them over each other to create a loop(though probably a much more complicated pattern), and then pull them together at relavistic speeds to close the loop, and then fly a ship through the loop at exactly the right speed/angle, you might then manage to make a closed timelike curve and travel to a younger universe. https://arxiv.org/pdf/hep-th/0502242.pdf Of course, the paper says that even a single graviton is enough to destabilize the ctc, so good luck.

The stars might be gone, but the photons they emitted during their life will mostly still be traveling in the universe.

To get energy you need photons, not star.

Build huge mirrors, send them out in the universe with FTL spaceships and harvest the light they send back. By wisely scattering the mirrors over several distances you will get plenty of energy for about the same age of the universe

Develop Superintelligence First

the only thing that makes sense to
do is to increase the scope and scale of human consciousness
- Elon Musk

The perspective of the human species will change dramatically in the coming centuries as it has in the 20th century (Before 1923 we thought our universe was just the Milky Way.)

Only last year Svante Paabo sequenced the Genomes of Neandertals and Denisovians. Sentient humanoids that roamed Europe 40 000 years ago. Many secrets still remain out there in the darkness of "unknown unknowns".

If we unlock the secret sauce of how our brains work. We will know how to increase our "intelligence" significantly and use the increase to further increase our intelligence.

Our Superintelligent descendants will understand Physics much better than we do.

In the mean time let us focus on reaching the critical mass of science, technology and wisdom required.

$\begingroup$But what is about the few dozen humans orbiting the last star?$\endgroup$
– J_F_B_MFeb 4 '16 at 10:09

$\begingroup$I think that humans should approach the question of surviving the death of our universe by first evolving super intelligence$\endgroup$
– Conor CosnettFeb 4 '16 at 10:54

1

$\begingroup$While technically true, humans should do a lot of things before even worse things happen, yet they are still regularly surprised by those worse things.$\endgroup$
– J_F_B_MFeb 4 '16 at 18:56

What if time was circular and life goes around the wheel of time. Space and time could be virtual and perception is the pointer on the space time co-ordinates. Ahh! the illusion of the expanding Universe, expanding into what? where will it expand into and what if the universes of a multiverse collection were all expanding at the same time? Would there be space for any to expand? Or would they slide under on into another universe via a black hole (or some other construct) much like tectonic plates do? Our understanding needs to expand to understand the expansion of the Universe... Also our observations have a time lag limited by the speed of light and the limits of our knowledge and tools. Aren't humans part of the Universe? How could they Universe have a heat death when humans have heat in their bodies? Maybe it's the death of the Universe due to high heat much like a heat stroke?

I didn't see this in one of the other 20 (!) answers: You cannot avoid the eventual heat death, but you can postpone it for yourself. Build a self-sustaining spaceship as your last home, board it and accelerate it as close to lightspeed as you get, closer and closer. You will live "forever" because of time dilation.

There is a requirement, and a problem.

The requirement is that there must be sufficient energy available to build such a ship, and to create the high-energy fuel which is needed to propel it. But because you have a planet orbiting a sun, there is plenty of energy. (BTW, I'm not sure how you arrive at a time scale of 10 years if you still have a whole frigging solar system, no matter how old ist sun is. The more "realistical" scenario is that the last black hole within reach is about to evaporate. No stars, no planets, just background radiation everywhere else.)

The problem is that "self-sustaining" is an unreachable ideal. The ship leaks energy, actually at an alarming rate while it is being propelled. The days of the crew are therefore numbered, because obviously there is no gas station anywhere. What's being extended is their life span measured from the "stationary" universe. If they get close enough to lightspeed they'll see much more of the universe's history than if they had stayed in place. (A history which is boring though.)

Their life span in the spaceship as it is individually perceived is actually (much) shorter because they are burning all this valuable energy in their lighspeed drive. They could have used all the energy much more efficiently in a well-isolated stationary survival station, and survived for eons harnessing the kinetic and gravitational energy of their solar system, long after the sun had burnt out. Perhaps you can make the group split, and in the end the space-farers come back and re-unite with the descendants of their fellows back then.

Create a new universe.

One cannot (by definition!) survive the heat death of the universe. And there may be no others to goto, and time travel into the past before the time machine was made may not be possible.

But one might be able to create a new universe.

I have had the idea that "The Big Bang has happened before. It can happen – or be made to happen – again". This is based on various ideas, such as the one by Stephen Hawking (in an older one of his books) that the Big Bang was triggered by a spontaneous fluctuation.

The key idea behind this is that cosmic inflation could produce the entire (currently) observable universe from a tiny amount of matter. Furthermore, in this model, the Big Bang can be triggered. Since our protagonists have had literally trillions of years of technological advancement behind them, we can assume they can trigger another.

The other part is creating somewhere to hide. I suspect that a wormhole into the newborn universe could suffice, if one end was sufficiently pinched off until the new universe had cooled to survivable levels. The throat of the wormhole could be a hiding place.

This theory also explains the fine-tuning needed for life – the Universe self-replicates, with the help of intelligent life, and thus is subject to Darwinian selection. Discovering this could be an interesting plot point.

You can't, but not in the traditional sense.

The last star burning out is not even close to the heat death of the universe. There is zero distance in heat at all; there is no temperature difference, and thus you cannot perform any work. Essentially, the universe is in thermodynamic equilibrium. (Perfectly balanced, as all things should be?)

The last star burning out is several orders of magnitude earlier than the heat death of the universe. After the last star dies, there will still exist billions of nebulas, planets, and other relatively static objects.

The fact that humans are still alive in your scenario (assuming normal humans) implies that it's been under 100 years since the star burned out. The heat death of the universe is far away.